Flexural Behavior of Prestressed Girder With High Strength Concrete

7/31/2019 Flexural Behavior of Prestressed Girder With High Strength Concrete

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ABSTRACT

CHOI, WONCHANG. Flexural Behavior of Prestressed Girder with High Strength Concrete.(Under the direction of Dr. Sami Rizkalla)

The advantages of using high strength concrete (HSC) have led to an increase in the typical

span and a reduction of the weight of prestressed girders used for bridges. However, growing

demands to utilize HSC require a reassessment of current provisions of the design codes. The

objective of one of the research projects, recently initiated and sponsored by the National

Cooperative Highway Research Program (NCHRP), NCHRP Project 12-64, conducted at

North Carolina State University is to extend the use of the current AASHTO LRFD design

specifications to include compressive strength up to 18,000 psi (124 MPa) for reinforced and

prestressed concrete members in flexure and compression. This thesis deals with one part of

this project. Nine full-size AASHTO girders are examined to investigate the behavior of

using different concrete compressive strength and subjected to the flexural loadings. The

experimental program includes three different configurations of prestressed girders with and

without a deck slab to investigate the behavior for the following cases: 1) the compression

zone consists of normal strength concrete (NSC) only; 2) the compression zone consists of

HSC only; and 3) the compression zone consists of a combination of two different strengths

of concrete. An analytical model is developed to determine the ultimate flexural resistance

for prestressed girders with and without normal compressive strength concrete. The research

also includes investigation of the transfer length and the prestress losses of HSC prestressed

girders. Based on materials testing and extensive data collected from the literature, a new

equation is proposed to calculate the elastic modulus for normal and high strength concrete.


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FLEXURAL BEHAVIOR OF PRESTRESSED GIRDER

WITH HIGH STRENGTH CONCRETE

By

Wonchang Choi

A dissertation submitted to the Graduate Faculty of

North Carolina State Universityin partial fulfillment of the

requirement for the degree ofDoctor of Philosophy

Civil Engineering

Raleigh, North Carolina

2006

Approved by:

Dr. Sami Rizkalla

Chair of Advisory Committee

Civil Engineering

Dr. Paul Zia

Advisory Committee

Civil Engineering

Dr. Amir Mirmiran

Advisory Committee

Civil Engineering

Dr. Kara Peters

Advisory Committee

Mechanical Engineering


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UMI Number: 3247018

3247018

2007

Copyright 2007 by

Choi, Wonchang

UMI Microform

Copyright

All rights reserved. This microform edition is protected againstunauthorized copying under Title 17, United States Code.

ProQuest Information and Learning Company300 North Zeeb Road

P.O. Box 1346Ann Arbor, MI 48106-1346

All rights reserved.

by ProQuest Information and Learning Company.


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BIOGRAPHY

Wonchang Choi obtained a Bachelors Degree in Chemistry from Kyung Hee University,

and a second Bachelors Degree in Civil Engineering from Hongik University, Seoul Korea.

He continued his studies in structures and completed research with the use fiber reinforced

polymer girder for compression members, completing his Masters Degree in 2002.

In 2003, he relocated to Raleigh, North Carolina State University under the supervision of Dr.

Sami Rizkalla to pursue his Doctor of Philosophy.


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ACKNOWLEGEMENTS

It would have been impossible to complete this dissertation without the intellectual,

emotional and financial support and friendship of my advisor, my colleague and my family.

It is with sincere gratitude that I thank my advisor, Dr. Sami Rizkalla, for his continuous

supervision and mentoring. I would also like to thank Dr. Paul Zia for providing valuable

insight. It is truly an honor to work with such an outstanding man who is willing to share his

wealth of knowledge and his extensive personal experience. Thanks are extended to Dr. Amir

Mirmiran for providing an opportunity to join this research program.

The technical assistance provided by the staff of the Constructed Facilities Laboratory (Bill

Dunleavy, Jerry Atkinson, and Amy Yonai) are greatly appreciated. Thanks are extended to

all of my fellow graduate students at the Constructed Facilities Laboratory for their help and

friendship. Special thanks are extended to Mina Dawood, as my officemate who was a

tremendous help to encourage me.

And lastly, I sincerely thank my parent and my lovely wife. I couldnt imagine standing here

without their unconditional love and support.

I know that this thesis is not the conclusion, but rather the starting point.


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TABLE OF CONTENTS

LIST OF FIGURES ............................................................................................................v

LIST OF TABLES ............................................................................................................vii

1 INTRODUCTION.......................................................................................................1

1.1 GENERAL ...............................................................................................................11.2 OBJECTIVES............................................................................................................2

1.3 SCOPE ....................................................................................................................3

2 LITERATURE REVIEW ...........................................................................................6

2.1 INTRODUCTION.......................................................................................................62.2 MATERIAL PROPERTIES ..........................................................................................8

2.3 STRESS BLOCK PARAMETERS................................................................................12

2.4 PRESTRESS LOSSES ...............................................................................................142.5 FLEXURAL BEHAVIOR OF GIRDERS WITH HIGH STRENGTH CONCRETE....................16

3 EXPERIMENTAL PROGRAM ...............................................................................18

3.1 INTRODUCTION.....................................................................................................183.2 DESIGN OF THE TEST SPECIMENS...........................................................................18

3.3 FABRICATION OF TEST SPECIMENS ........................................................................223.4 INSTRUMENTATION ...............................................................................................29

3.5 MATERIAL PROPERTIES ........................................................................................353.6 FLEXURAL TEST DETAILS .....................................................................................45

4 RESULTS AND DISCUSSION ................................................................................54

4.1 INTRODUCTION.....................................................................................................544.2 MATERIAL PROPERTIES STUDY .............................................................................554.3 PRESTRESS LOSSES ...............................................................................................65

4.4 TRANSFER LENGTH...............................................................................................724.5 CAMBER...............................................................................................................74

4.6 FLEXURAL RESPONSE ...........................................................................................75

5 ANALYTICAL MODEL ........................................................................................100

5.1 INTRODUCTION...................................................................................................1005.2 CODE PROVISONS ...............................................................................................101

5.3 SECTION ANALYSIS ............................................................................................120

6 SUMMARY AND CONCLUSIONS....................................................................... 135

6.1 SUMMARY ..........................................................................................................1356.2 CONCLUSIONS ....................................................................................................136

6.3 RECOMMENDATION AND FUTURE WORK .............................................................140


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LIST OF FIGURES

Figure 3-1 Cross-section showing prestressing strand configurations...................................21Figure 3-2 Prestressing bed: a) Elevation schematic view of prestressing bed, b) Strand lay-

out, c) Pretensioning ..........................................................................................24

Figure 3-3 Sequence of girder fabrication............................................................................26Figure 3-4 Formwork for the 5 ft. and 1 ft. wide deck slabs.................................................28Figure 3-5 Load cell installation..........................................................................................30

Figure 3-6 Locations of weldable strain gauges...................................................................33Figure 3-7 Installation of weldable strain gauge ..................................................................34

Figure 3-8 Installation of the strain gauges attached to #3 steel rebar...................................35Figure 3-9 Specimen preparation and test set-up for elastic modulus ................................... 39

Figure 3-10 Test set-up for elastic modulus and modulus of rupture....................................40Figure 3-11 Material property for prestressing strand .......................................................... 44

Figure 3-12 Test set-up schematic .......................................................................................45Figure 3-13 Typical test set-up for nine AASHTO girder specimens ................................... 46

Figure 3-14 Location of LMTs to measure deflections.........................................................49Figure 3-15 Location of Strain and PI gages for 10PS 5S, 14PS- 5S and 18PS-5S ............ 50

Figure 3-16 Location of Strain and PI gages for 10PS1S, 14PS-1S and 18PS-1S............... 51Figure 3-17 Location of Strain and PI gages for 10PS-N, 14PSN and 18PS-N................... 53

Figure 4-1 Comparison of the elastic modulus between test results and predicted value.......57

Figure 4-2 Comparison between predicted E and measured E with various equations; a)AASHTO LRFD and ACI318; b)ACI363R; c) Cooks; d) Proposed.................. 59

Figure 4-3 Normal distribution for the ratio of predicted to measured elastic modulus.........62Figure 4-4 Modulus of rupture versus compressive strength ................................................ 64

Figure 4-5 Load-deflection behavior for 10, 14, 18PS-5S....................................................76Figure 4-6 Strain envelopes for 18PS-5S.............................................................................78

Figure 4-7 Moment N.A. depth location for 10PS 5S, 14PS 5S and 18PS 5S ........... 80Figure 4-8 Typical failure mode for the AASHTO girder with a 5 ft. wide deck.................. 81

Figure 4-9 Load-deflection behavior for 10PS 1S, 14PS 1S and 18PS-1S ...................... 84Figure 4-10 Strain envelopes for 10PS-1S ...........................................................................86

Figure 4-11 Moment N.A. depth location for 10PS 1S, 14PS 1S and 18PS 1S .........88Figure 4-12 Typical failure modes for the AASHTO girder with a 1 ft. wide deck...............90

Figure 4-13 Load-deflection behavior for 10PS - N, 14PS N and 18PS-N.........................92Figure 4-14 Strain envelopes for 18PS-N ............................................................................94

Figure 4-15 Moment N.A. depth location for 10PS - N, 14PS N and 18PS - N ..............96Figure 4-16 Typical failure modes for the AASHTO girder without deck............................97

Figure 4-17 Ultimate strain at peak load for tested AASHTO girders .................................. 99

Figure 5-1 Cracking strength ratio for three different calculations .....................................104Figure 5-2 Compressive stress distribution (a) cross-section; (b) strain compatibility; (c)

meausred strain-stress distribution in compression zone; (d) the equivalentrectangular stress block in compression zone ................................................... 111


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Figure 5-3 Compressive stress distribution (a) cross-section; (b) strain compatibility (c)measured strain-stress distrubution in compression zone, (d) simplified stress

distribution (e) the equvalent rectagular stress block ........................................ 114Figure 5-4 Compressive stress distribution (a) cross-section; (b) strain compatibility; (c)

measured strain-stress distribution in compression zone; (d) the equivalent

rectangular stress block.................................................................................... 116Figure 5-5 Failure evaluation for each configuration ......................................................... 118Figure 5-6 Cross-section and assumed strain profile for 18PS - 5S.................................... 121

Figure 5-7 Measured stress-strain behavior of 10PS-5S and a best-fit curve with analyticalmodel...............................................................................................................124

Figure 5-8 Definition of the four factors adopted from Collins (1997) ...............................127Figure 5-9 Analytical modeling of the prestressing strand .................................................127

Figure 5-10 Measured and predicted load deflection responses..........................................130Figure 5-11 Measured and predicted load deflection responses..........................................131

Figure 5-12 Measured and predicted load deflection responses..........................................132Figure 5-13 Flexural strength ratio of the measured versus predicted results...................... 134


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LIST OF TABLES

Table 3.1 Detailed Design of the Test Specimens ................................................................ 20Table 3.2 Construction Sequence Summary ........................................................................23

Table 3.3 Measured Data from Load Cells ..........................................................................31

Table 3.4 Order of Prestressing Strands and Elongation ...................................................... 32Table 3.5 Detailed Mix Design for Girder Specimens..........................................................36Table 3.6 Concrete Properties for Girder Specimens............................................................37

Table 3.7 Concrete Mix Design for Deck Slab.....................................................................38Table 3.8 Concrete Properties for Cast-in-place Deck..........................................................38

Table 3.9 Test Results for Material Properties .....................................................................42Table 3.10 Compressive Strength Test for Deck Concrete...................................................42

Table 3.11 Material Property for Each AASHTO Girder Specimen.....................................43

Table 4.1 Range of the Collected Data ................................................................................58Table 4.2 Results of Statistical Analysis ..............................................................................61

Table 4.3 Elastic Shortening at Transfer ..............................................................................68Table 4.4 Creep and Shrinkage Prediction Relationships by AASHTO LRFD.....................70

Table 4.5 Test Results for Prestressed Losses at Test Day...................................................71Table 4.6 Summary of End Slippage and Transfer Length...................................................73

Table 4.7 Summary of Camber Results ...............................................................................74Table 4.8 Observed Test Results for 10PS5S, 14PS5S and 18PS-5S................................76

Table 4.9 Observed Test Results for 10PS-1S, 14PS1S and 18PS-1S.................................84Table 4.10 Observed Test Results for 10PS-N, 14PSN and 18PS-N .................................. 93

Table 5.1 Comparison between Observed and Computed Cracking Strength ..................... 103

Table 5.2 Calculation Method for the Flexural Strength .................................................... 106Table 5.3 Comparison of Design Calculation ....................................................................110

Table 5.4 Design Calculations for Composite AASHTO Girders.......................................112Table 5.5 Design Calculation for Composite AASHTO Girders ........................................ 115

Table 5.6 Design Calculation for AASHTO Girders without a Deck ................................. 117Table 5.7 Failure Evaluation for All Specimens.................................................................119

Table 5.8 Concrete Material Model for the Specimens ...................................................... 125


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Chapt er 1 Introduction

1

1 INTRODUCTION1.1 GENERAL1.1.1 High Performance versus High Strength ConcreteThe performance of concrete has been improved through the use of chemical and mineral

admixtures such as fly ash, slag, silica fume, and high-range water reducing agents. These

admixtures have the potential to influence particular properties of concrete and, as such,

influence the compressive strength, control of hardening rate, workability, and durability of

the concrete. Thus, more rigid criteria are needed to define the performance of concrete.

Zia (1991), in a study undertaken through the Strategic Highway Research Program (SHRP),

defines high performance concrete (HPC) by using three requirements: a maximum water-

cementitious ratio less than 0.35; a minimum durability factor of 80 percent, and a minimum

compressive strength. Russell (1999) states that HPC in the ACI definition is that concrete

meeting special combinations of performance and uniformity requirements that cannot

always be achieved routinely using conventional constituents and normal mixing, placing,

and curing practices. Neville (4th

Edition) specifies that HPC includes two major properties,

high compressive strength and low permeability.

The term, high performance concrete, may be a more comprehensive expression than high

strength concrete. However, this project focuses on the behavior of high compressive

strength. Therefore, instead ofhigh performance concrete, the term, high strength concrete

(HSC), is used in this study.


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1.1.2 High Strength ConcreteResearch by Carasquillo et al. (1981) on HSC highlighted the uncertainty and potential

inaccuracy of using current code provisions that have been developed for normal concrete

strength. Accordingly, several studies have been conducted to gain a better understanding of

HSC flexural members including prestressed concrete girders. However, the definition and

boundaries of HSC contain too many ambiguities to specify stringent conditions. Therefore,

many specifications mainly specify the compressive strength for HSC. According to the ACI

363R State-of the Art Report on High Strength Concrete (1992), the definition of HSC is

based on the compressive strength of 6,000 psi (41 MPa) or greater at the age of 28-day.

However, one must note that the definition of HSC has changed over the years and will no

doubt continue to change.

1.2 OBJECTIVESThe main objective of this research is to evaluate the behavior of prestressed concrete girder

with high strength concrete with and without a cast-in-place normal strength deck slab. The

specific objective can be summarized as follows:

1. Due to the lack of complete knowledge of the material properties of HSC, theprediction of the material properties using current design specifications may be

inaccurate in determining the behavior and the strength. This may include unreliable

predictions of the cracking strength and ultimate flexural strength. This introduced the


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needs for reassessment of the material properties of HSC using more accurate test

results.

2. This research program proposes to validate the analytical models typically used todetermine the flexural response of prestressed HSC AASHTO type girders with and

without a cast-in-place normal strength deck. The intent of the tests is to validate the

use of stress block parameters in calculating the flexural resistance of flanged sections

with HSC. This experiment also investigates the effect of the presence of normal

strength deck in composite action with HSC girders.

3. Evaluate the applicability of the current code equations to predict the prestress lossesin HSC girders, including recently proposed equations by Tadors (2003), based on the

measured prestress losses of prestressed concrete girders.

4. Provide recommendations for the design of prestressed concrete girders with HSC.

1.3 SCOPETo study the behavior and prestress loss of prestressed high strength concrete girder, a total

of nine AASHTO type II girders were tested with and without normal strength concrete deck

slab.

All girders were simply supported with 40 ft. long. The nine AASHTO Type II girders were

fabricated and tested up to failure under static loading conditions using four-point loading.


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Three girders were cast without a concrete deck. Therefore, the entire section consists of

HSC only. The rest of the girders were cast with a concrete deck. The concrete decks were

cast at the Constructed Facilities Laboratory (CFL) at North Carolina State University,

Raleigh, NC after the girders were fabricated. The design concrete strengths for the nine

girders ranged from 10,000 psi (69 MPa) to 18,000 psi (124 MPa). The concrete strength of

the cast-in-place deck was in the range of 4,000 psi (28 MPa).

The flexural response of the prestressed girders was investigated in a three-phase

experimental research program. In the first phase, three HSC AASHTO with three different

target strength and a cast-in-place NSC deck were fabricated. This allowed the compression

zone will be located within the NSC deck slab. In the second phase, included three

prestressed girders with HSC and the narrow width cast-in-place NSC deck. Therefore, the

compression zone consists of HSC and NSC. In the third phase, three prestressed girder with

HSC without deck slab was subjected to flexure to study the behavior when the entire

compression zone consisted of HSC only.

The nine girders were extensively instrumented to measure the different limit states including

cracking and deflections at various loading stages, as well as prestress losses measurements.

The research includes modeling of the behavior of the prestressed girders based on strain

compatibility and equilibrium approach. The measured values were also compared to the

predictions according to code equations. Based on the findings, design model is proposed for

the prediction of the ultimate moment resistance of HSC prestressed girders.


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Chapter 2 of this thesis presents a relevant literature review of the flexural behavior of

prestressed AASHTO girders with HSC. The literature review includes material properties,

stress block parameters, prestress losses, and the flexural behavior of HSC girders.

Chapter 3 of this thesis describes in details the experimental program, including design

considerations, fabrication procedures of the prestressed AASHTO girders, instrumentation,

the flexural test setup, and separate test results for each phase.

Chapter 4 summarizes the test results and discussion the material properties, transfer length,

prestress losses and flexural response of the tested girders under static loading conditions.

Chapter 5 presents the analytical model for the flexural behavior of the prestressed concrete

girders using HSC. A comparison of the measured and computed values is discussed.

The summary and conclusion of the research program are presented in Chapter 6.


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Chapt er 2 Literature Review

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2 LITERATURE REVIEW2.1 INTRODUCTIONHigh strength concrete has been used and studied as a workable construction material for

several decades. In the United States, HSC was applied to major prestressed girders in 1949.

Walnut Lane Bridge in Philadelphia was the first bridge reported to use HSC in its design

and construction (Russell, 1997). This bridge was constructed with a 160 ft. center main span

with two 74 ft. side spans. The required strength of 5,400 psi (37 MPa) was obtained in 14 to

17 days. Zollman (1951) reported that the compressive strength at 28 days was usually high

about 6,500 psi (45 MPa). ACI 363R-97 notes that concrete with a compressive strength of

5,000 psi (34 MPa) was considered to be HSC in the 1950s. However, at about that same

time, the introduction of prestress design methods would have been considered to be more

remarkable than the use of HSC. The development of high-range water reducing admixtures

in the 1960s and further improvements of material technology increased the possibilities for

HSC production in the construction industry.

From the late 1970s, the major research into the application of prestressed bridge girders

using HSC was conducted at Cornell University, the Louisiana Transportation Research

Center, the University of Texas at Austin, North Carolina State University, the Portland

Cement Association and Construction Technology Laboratory, the Minnesota Department of

Transportation and others. In general, this research focused on three subjects: the

development of concrete mix designs to produce HSC using regional materials; the

assessment of equations used to predict the material properties of HSC; and the application of

prestressed girders with HSC, including cost effectiveness.


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Additional research (Law and Rasoulian, 1980; Cook, 1989; Adelamn and Cousins, 1990)

shows that concrete compressive strength in excess of 10,000 psi (69 MPa) using regional

materials can be produced by the construction industry. In addition to mix design

development, an increase in concrete design compressive strength, from 6,000 psi (41 MPa)

to 10,000 psi (69 MPa), results in an average 10 percent increase in span capability for

prestressed girders used in routine bridge design (Adelamn and Cousins, 1990). For this type

of bridge construction, it has been shown that an increase in concrete strength and stiffness

can also result in increased cost effectiveness.

Concrete with a compressive strength of 10,000 psi (69 MPa) can now be routinely produced

commercially. Based on HSCs advantages, the application of prestressed girders with HSC

has increased in the United States. Moreover, the need for a reassessment of current design

code has broadened.

This section provides a description of selected test results and the design parameters for

predicting the flexural behavior of prestressed girders with HSC. Topics in this section

include: 1) material properties, 2) stress block parameters, 3) prestress losses and 4) the

flexural behavior of girders with HSC.


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2.2 MATERIAL PROPERTIESThe material properties of HSC constitute the essential factors in the design and analysis of

longer bridge spans due to the increasing use of HSC in such bridge design. A more accurate

prediction methodology for the material properties of HSC is required to determine prestress

losses, deflection and camber, etc. Many researchers have proposed methods for the

prediction of material properties for HSC. This section addresses the major findings related

to the material properties for HSC.

2.2.1 Pauw (1960)The ACI Committee 318 Building Code (ACI 318-77) has accepted the findings of Pauw

(1960) for the elastic modulus. Pauw utilized other researchers test results for the modulus

of elasticity and derived the empirical equation for normal-weight concrete by using the least

squares method based on a function of the unit weight and compressive strength of concrete.

The proposed empirical modulus of elasticity, Ec, equation shows good agreement for the

normal-weight concrete. These equations are recommended in the current ACI 318 Building

Code and in the AASHTO LRFD specifications. They are given as:

( ) 5.05.133 cc fwE = (psi) and Equation 2-1

( ) 5.05.1043.0cc

fwE =(MPa) , Equation 2-2

where

wc = dry unit weight of concrete at time of test;

fc' = compressive strength of concrete.


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2.2.2 Carasquillo et al. (1981)Research into HSC was conducted at Cornell University by Carasquillo et al. (1981). The

ACI Committee 363s State-of-the-Art Report of High-Strength Concrete (ACI 363R-84

1984) accepted the findings of their research as well as their proposed equations for the

elastic modulus and the modulus of rupture for HSC. The Carasquillo team investigated the

compressive concrete strength range from about 3,000 to 11,000 psi (21 to 76 MPa).

Carasquillo et al. suggested that the ACI 318-77 equations, based on the proposal of Pauw

(1960), overestimate the modulus of elasticity for HSC ranging from 6,000 psi (41 MPa) or

more because the stiffness of the concrete is due to a combination of mortar and aggregate

strength. The Carasquillo study also discusses the effects of coarse aggregate type and

proportions on the modulus of rupture and the modulus of elasticity. However, no

consideration was given to the effects of the use of different aggregates on the modulus.

Regarding the Poissons ratio of concrete, Carasquillo et al. state that the value of Poissons

ratio of concrete is close to 0.2 regardless of the compressive strength or the age of the test.

Currently, ACI 363R-97 relates these properties to the specified compressive strength

ranging from 3,000 psi (21 MPa) to 12,000 psi (83 MPa) and still accepts the Carasquillo

research results. The equations are given below for the elastic modulus, Ec and modulus of

rupture,frare;

( ) ( ) 5.165.0 14510000,40 ccc wfE += (psi), Equation 2-3

( ) ( ) 5.15.0 23206900320,3 ccc wfE += (Mpa), Equation 2-4

cr ff = 7.11 (psi) and Equation 2-5


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cr ff = 94.0 (Mpa) Equation 2-6

2.2.3 Ahmad and Shah (1985)Empirical equations for the material properties of HSC were derived from experimental data

from other researchers. The research of Ahmad and Shah is limited to compressive concrete

strength up to 12,000 psi (84 MPa). Ahmad and Shah found that the difference in the

characteristics of the stress-strain curve between NSC and HSC is significant. They also

stated that the modulus of rupture of HSC in ACI318-83 is very conservative, while the

modulus of elasticity in ACI318-83 computes 20 percent higher values. Ahmad and Shah

suggested new equations for the modulus of rupture and the modulus of elasticity of HSC.

The equations are given below as reference.

( ) 325.05.2 ccc fwE = (psi) , Equation 2-7

( )

325.05.25

10385.3 ccc fwE =

(MPa), Equation 2-8

( ) 322 cr ff = (psi) and Equation 2-9

( ) 3238.0cr

ff =(MPa). Equation 2-10

2.2.4 Zia et al. (1993)The Strategic Highway Research Program on mechanical behavior of high performance

concrete was conducted by Zia et al. at North Carolina State University. The concrete

specimens referred to as Very High Strength show 28-day compressive strengths ranging


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from 8,080 to 13,420 psi (55.7 to 92.5 MPa). Based on Zia et al.s research findings, the test

results correlate well with the ACI 318 equation for the elastic modulus, which is similar to

the AASHTO LRFD. Zia et al. (1993) found that the equation in ACI 363R, developed by

Carasquillo et al. (1981), underestimates the measured elastic modulus. For the modulus of

rupture, they found that at the design age, the ratio of the observed value to the value

predicted by ACI 318 is 1.06 for concrete made with fly ash and 1.15 for concrete made with

silica fume. In a comparison of the modulus rupture between the measured values and those

predicted by ACI 363R, the ratio is as low as 0.68.

2.2.5 Mokhtarzadeh and French (2000)More recent research has been conducted by Mokhtarzadeh and French (2000). Their

research included extensive test results and predictions regarding the material properties for

HSC. They conducted tests using 98 mixtures with compressive strengths ranging from 6,000

to 19,500 psi (41.4 to 135 MPa) for the modulus of elasticity and 280 modulus rupture beams

made from 90 HSC mixtures with compressive strengths ranging from 7,500 to 14,630 psi

(51.7 to 101 MPa), including heat-cured and moist-cured conditions. Their data showed that

the ACI 318-99 equation overestimates the elastic modulus of HSC, while the ACI 363R-92

equation provides a more reasonable prediction of the elastic modulus for moist-cured

specimens and slightly overestimates heat-cured test results. For the modulus of rupture,

Mokhtarzadeh and French found that values measured for the moist-cured specimens are

adequately predicted by the ACI 363R-92 equation. Values from the heat-cured specimens

fall in between the values predicted by the ACI 363R-92 and ACI 318-99 equations. The

authors proposed a new relationship for the modulus of rupture that uses a coefficient of 9.3

in lieu of the 7.5 in the ACI 318 equation.


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2.3 STRESS BLOCK PARAMETERSThe equivalent rectangular stress block has been widely used to determine the ultimate

flexural strength of reinforced and prestressed beams and columns. Through the application

of ultimate strength design theory, stress block parameters have been developed to make

equivalent rectangular stress blocks that can simplify the actual stress distribution. The

proposed stress block by many researches are given in Appendix A. This section presents

major findings in the use of stress block parameters for predicting the ultimate flexural

strength.

2.3.1 Mattock et al. (1961)The ACI 318 and AASHTO LRFD specifications regarding the use of stress block

parameters to compute flexural strength were originally developed by Mattock et al. (1961).

The Mattock research used studies previously conducted by Whiney (1937) and Hognestad et

al. (1995) as reference. Mattock et al. suggested the use of stress block parameters, 1 and 1,

to determine ultimate strength and 1 is taken as 0.85 of the cylinder strength; 1 is taken as

0.85 for concrete cylinder strength up to 4,000 psi (28 MPa); and thereafter is reduced by

0.05 for each 1,000 psi of strength in excess of 4,000 psi. Based on design examples for

bending and compression, they concluded that the proposed stress block parameters allow

sufficient accuracy of the prediction of ultimate strength in bending and compression.


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2.3.2 Nedderman (1973)In Neddermans research (1973), plain concrete columns with compressive strengths up to

14,000 (98 MPa) were tested under eccentric loading conditions. Nedderman suggests that

the depth of the stress block, 1 in ACI318 (ACI 318, 1971), becomes an unrealistic value at

a compressive concrete strength of 21,000 psi (147 MPa). This research also proposes the

lower limits of1 to be 0.7 with a compressive concrete strength higher than 7,000 psi (49

MPa).

2.3.3 Ibrahim et al. (1996, 1997)In the Ibrahim research, 20 HSC columns up to 14,500 psi (100 MPa) and UHSC with

the compressive concrete strength over 14,500 psi were tested that incorporates concrete

strength, confinement steel, and the shape of the compression zone. The test specimens

consisted of fourteen C-shaped sections with a rectangular cross-section and six C-

shaped sections with a triangular section. A better understanding of the flexural behavior

of HSC and UHSC sections without confinement or with less confinement than required

in seismic regions was also sought in this test. The Ibrahim study concluded that the ACI

stress block parameters (ACI 318, 1989) overestimate the moment capacity of HSC and

UHSC columns in compression. The researchers proposed new stress block parameters,

as follows:

c

c ff = 725.0800

85.01(MPa) and Equation 2-11

c

c ff

= 70.0400

95.01(MPa). Equation 2-12


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2.4 PRESTRESS LOSSESConcrete is a time-dependent material. In particular, concrete experiences creep under a

sustained load and experiences shrinkage due to changes in moisture content. These physical

changes increase over time. The prestress losses due to concrete creep and shrinkage result in

the loss of compressive force onto the concrete. Ngab et al. (1981) measured less creep and

slightly more shrinkage of HSC in comparison to NSC. The creep coefficient for HSC was

50 to 70 percent that of NSC. In a similar study, Nilson (1985) found that the ultimate creep

coefficient for HSC is much less than that of NSC. This section describes findings regarding

the prestress losses of full-size prestressed girders with HSC.

2.4.1 Roller et al. (1995)A project undertaken in Louisiana investigated prestress losses in HSC girders. Two bulb-tee

sections, 70 ft. (21.3 m) long and 54 in. (1372 mm) deep and designed according to

AASHTO standard specifications (AASHTO 1992), were tested for long-term study. The

design compressive strength at 28 days for the girders concrete and releasing strength was

10,000 psi (69MPa) and 6000 psi (41 MPa), respectively. The concrete strain due to prestress

losses of the girders was measured using internal Carlson strain meters under the full design

dead load for 18 months. Roller et al. concluded that concrete strains measured at 28 days

indicate that prestress losses are significantly less that the losses calculated using the

provisions found in the AASHTO standard specifications.

2.4.2 Tadros (2003)A more recent published study, National Cooperative Highway Research Program (NCHRP)

Report 496 by Tadros (2003), developed design guidelines for estimating prestress losses in

Documents

Flexural Behavior of Prestressed Girder With High Strength Concrete